Wendy borrows $$5,000$ two years before graduation at $7\%$ interest. She has until $10$ years after graduation to complete her payments, which she will make monthly. Unless otherwise stated, assume the full allowable time is used to complete payments.

a$.$ Suppose Wendy makes her payments at the beginning of each month. If she starts making payments six months after she graduates, how much will her payments be and how much total interest will she pay?

b$.$ Suppose Wendy is lucky enough to receive $$1,000$ at the time of graduation. If she makes a one$-$time $$1,000$ payment toward her loan and starts making payments at the end of each month as soon as she graduates, how much will her payments be and how much total interest will she pay?